Use a trial-and-error approach in Matlab to determine the ultimate controller gain Kcu and the ultimate period Pu for control of a FOPDT process with a deadtime of 30 seconds and

a process time constant of 50 s. Use the Ziegler-Nichols rules to tune a PI controller, providing Kc and reset time. Plot (a) the open loop response to a step-change in setpoint without control (b) the closed loop response to a step-change in setpoint without control, and (c) plot the closed-loop response to a step-change in setpoint with the ZN tuned controller.